Question

Assertion :If $\Delta \left(x\right)=\left|\begin{array}{cc}{f}_1\left(x\right)& f_2\left(x\right)\\ g_1\left(x\right)& g_2\left(x\right)\end{array}\right|$, then ${\Delta }^{\prime }\left(x\right)\ne \left|\begin{array}{cc}{f}_1^{\prime }\left(x\right)& f_2^{\prime }\left(x\right)\\ g_1^{\prime }\left(x\right)& g_2^{\prime }\left(x\right)\end{array}\right|$ Reason: $\frac{d}{dx}\left\{f\right(x\left)g\right(x\left)\right\}\ne \frac{d}{dx}f\left(x\right)\frac{d}{dx}g\left(x\right)$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Explanation: the given assertion shows that differentiation of the determinant of the $a$ equation is not equal to the differentiation of its individual elements of the determinants

Because the reason is that the differentiation of the product of two functions are not same as the product of its individualize differntialized functions.

Since the assertion and reasons are correct and the reason explains the assertion well.

Hence Option A is the correct Answer